The two scriptures you have quoted give us the core of what righteousness actually is. I firmly believe the second scripture which gives us the faith to believe that when we accepted Jesus as Saviour we immediately became as righteous as He is. We never earned it. We were made the righteousness of God in Christ. The righteousness is interwoven with our faith in Jesus. That is the message of your first scripture. So how do we interpret that in practical terms? It is this:
We can stand before God without any sense of shame, guilt, or sin consciousness. We can do great things for Him and with Him, because the sin consciousness that would hold us back is now gone completely.
The word “there is none righteous, no not one” is the state of people before they accept Christ. After accepting Christ it is a whole different story.